Embedded Cobordism Categories and Spaces of Submanifolds

@article{RandalWilliams2010EmbeddedCC,
  title={Embedded Cobordism Categories and Spaces of Submanifolds},
  author={Oscar Randal-Williams},
  journal={International Mathematics Research Notices},
  year={2010},
  volume={2011},
  pages={572-608}
}
  • O. Randal-Williams
  • Published 13 December 2009
  • Mathematics
  • International Mathematics Research Notices
Galatius, Madsen, Tillmann, and Weiss [7] have identified the homotopy type of the classifying space of the cobordism category with objects (d −1)-dimensional manifolds embedded in ℝ ∞ . In this paper we apply the techniques of spaces of manifolds, as developed by the author and Galatius in [8], to identify the homotopy type of the cobordism category with objects (d −1)-dimensional submanifolds of a fixed background manifold M. There is a description in terms of a space of sections of a bundle… 
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